Question: Solve for $x$ and $y$ using elimination. ${-x+4y = 27}$ ${x-5y = -35}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-x+4y = 27}\thinspace$ to find $x$ ${-x + 4}{(8)}{= 27}$ $-x+32 = 27$ $-x+32{-32} = 27{-32}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {x-5y = -35}\thinspace$ and get the same answer for $x$ : ${x - 5}{(8)}{= -35}$ ${x = 5}$